Dear Readers, Important Aptitude Questions for SSC CHSL Exam was given here with solutions, candidates those who are preparing for those exams can use this material.

Directions
(1-10): Find The value for the Given below Geometry Questions

1). A vertical pole and a vertical tower are
standing on the same level ground. Height of the pole is 10 metres. From the
top of the pole the angle of depression of the foot of the tower are 60o
and 30o respectively. The height of the tower is

a)20 m

b)30 m

c)40 m

d)50 m

2). Area of a regular hexagon with side ‘a’ is

a)[(3√3)/4] a2 sq. unit

b)[12/(2√3)] a2 sq. unit

c)[9/(2√3)] a2 sq. unit

d)[6/√2] a2 sq. unit

3). If the sum of the dimensions of rectangular
parallel piped is 24 cm and the length of the diagonal is 15 cm, then the total
surface are of its is

a)420 cm2

b)275 cm2

c)351 cm2

d)378 cm2

4). A horse takes 2 ½ seconds to complete a
round around a circular field. If the speed of the horse was 66 m/sec, then the
radius of the field is, { given π=22/7 }

a)25.62 m

b)26.52 m

c)25.26 m

d)26.25 m

5). A flask in the shape of a right circular
cone of height 24 cm is filled with water. The water is poured in a right
circular cylindrical flask whose radius 1/3 rd is of the radius of the base of
the circular cone. Then the height of the water in the cylindrical flask is

a)32 cm

b)24 cm

c)48 cm

d)72 cm

6). If the three medians of a triangle are
same, then the triangle is

a)Equilateral

b)Isosceles

c)Right-angled

d)Obtuse-angled

7). The external fencing of a circular path
around a circular plot of land is 33 m more than its interior fencing. The
width of the path around the plot is

a)5.52 m

b)5.25 m

c)2.55 m

d)2.25 m

8). The Perimeters of two similar triangles ∆ABC
and ∆PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, The AB is

a)15 cm

b)12 cm

c)14 cm

d)26 cm

9). If the sides of a right-angled triangle
are three consecutive integers, then the length of the smallest side is

a)3 units

b)2 units

c)4 units

d)5 units

10). Two circles intersect each other at the
point A and B, A straight line parallel to AB intersects the circles at C, D, E
and F. If CD = 4.5 cm, then the measure of EF is

a)1.50 cm

b)2.25 cm

c)4.50 cm

d)9.00 cm

Answers:

1).c) 2).c)
3).c) 4).d) 5).d) 6).a) 7).b) 8).a)
9).a) 10).c)

Solutions:

1).

In
∆ECB

tan
60o = BE/CE à √3 = BE/CE

BE = √3 CE
…………… (i)

In
∆ACD,

tan
30 = CD/DA

∆
1/√3 = 10/DA

DA
= 10√3

But
CE = DA = 10√3

(i)à BE = √3 CE

= √3 ×10√3
= 30m

Height
of the tower = AE + BE = 10 + 30 = 40m

Answer: c)

2).

Area
of an equaliteral triangle = √3 a2 / 4

Area
of regular hexagon

=
6 ×[ √3 a2 / 4 ]

=
[ 3√3 / 2 ]a2

=
[3√3 / 2] a2 × √3/√3

= 9 a2
/ 2√3 sq. unit

Answer: c)

3).

Let
the dimensions of the rectangular parallelepiped be x, y and z

Then
x + y + z = 24

Length
of the diagonal

√(x2+y2+z2)
= 15

x2 +y2
+ z2 = 225

Now , (x+y+z)2
= x2+y2+z2+2(xy+yz+zx)

(24)2
= 225+2(xy+yz+zx)

2(xy+yz+zx) = 576-225 =351

Total surface area = 2(xy+yz+zx) =
351 cm2

Answer: c)

4). Perimeter of the circle = Time taken ×
Speed

=
66 × 2 ½

=
66 × 5/2

=
33 × 5 = 165 m

2πr = 165

2 × 22/7 × r =
165

r = (165 × 7) / (2 × 22)

r = 26.25 m

Answer: d)

5).Let
the radius of the cone be R and height be H

Let
the radius and height of the cylinder be r and h

Then , Volume of the cylindrical flask = Volume of
the cone

π r2h
= 1/3 π R2H

(R/3)2h = 1/3 × R2
24

h = (R2×24×3×3)
/ (R2×3) = 72 cm

Answer: d)

6).
If three medians of a triangular are the same, then the triangle is equilateral

Answer: a)

7).

Let
the radius of the external circle and the internal circle be R and r
respectively